In the long battle against slavery in the 19th century, it was the voices of evangelical Christians such as William Wilberforce, John Wesley and Bishop of London Beilby Porteus who played an important role in swinging the domestic political debate in favour of abolition, alongside Quakers and others.

They did so because they realised that although there were verses in the Bible (for them the determining authority in life and conduct) that could readily be pressed into the defence of slavery, there was something much larger at stake in the Gospel message which led inexorably to the conclusion that the captives should be set free – as Jesus said in one of his defining sermons, as recorded by Luke.

On that basis they re-interpreted pro-slavery verses by understanding them as overwritten by the new order of grace brought about by Christ, as warnings about the partiality of human insight into the mystery of God's love, and as stage posts in a process of unfolding, deepening revelation.

Similar arguments are being heard today from a growing number of evangelical Christians over the question of recognising the civil, ecclesial and relationship status of lesbian and gay people. These evangelicals are still a minority, but they are a growing one. They bring to the challenge of changing the hearts and minds of their fellow believers the same moral and theological seriousness that motivated their forebears in the anti-slavery movement.

This week, four evangelical organisations have joined together to remind their fellow "Bible people" that opposing hate speech and hate crimes against homosexual people – in this case the antics of the bizarre Westboro Baptist sect – means too little if you are simultaneously defending forms of prejudice and discrimination within your own communities.

The prime mover in this, Accepting Evangelicals, is a network of Christians who take the Bible with great seriousness, but who argue that what the handful of verses deployed by anti-gay campaigners address is not modern same-sex relationships built on mutual commitment and self-giving love, but practices of pederasty, cultic prostitution and abuse in very different cultural and religious contexts.

They are supported in this view by considerable biblical scholarship and by Christians of other stripes who share the conviction that being followers of Jesus in the modern world involves responsible freedom not backward-looking fear.

The recent statement was also signed by the Network of Baptists Affirming Lesbian and Gay Christians, the Evangelical Fellowship for Lesbian and Gay Christians, the thinktank Ekklesia (which has many evangelicals involved with it, and of which I am co-director), and by Courage UK – an organisation that started out as an "ex-gay" ministry but which has now shifted towards acceptance and inclusion as a Gospel imperative.

Courage UK, founded in 1998, was pushed to resign from the Evangelical Alliance in 2002 as a result of its changed stance. Those who head up major evangelical organisations know that there are dissenters in their own ranks, but they fear the debate that would result if this was acknowledged more openly. The hardliners in their midst also find succour in being seen as part of a righteous war against a supposed "liberal" enemy intent on diluting the Gospel message. Similar arguments were used to try to rebut the abolitionists.

It is strange indeed that opposition to same-sex relationships has become a litmus test for a certain kind of orthodoxy in some evangelical circles, despite the fact that Christ said nothing about it. On the contrary, he deliberately breached religious taboos against groups ostracised by the establishment, and he upheld actions like forgiveness and economic sharing as signs of authentic discipleship – not culture-based religious restrictions.

Change is on the way, nonetheless. The refusal of a mature debate on sexuality is being questioned and jettisoned in many parts of the evangelical world: among young people involved in fresh "emerging" forms of church life, in discussions at festivals like Greenbelt, and even in the counsels of the heartlands.

Last November the highly respected Richard Cizik resigned as vice president for governmental affairs with the 50 million-strong National Association of Evangelicals in the USA, following uproar over his comments that he is shifting his views on same-sex unions.

In Britain, pro-gay evangelicals have also been "coming out". A few years ago veteran Methodist preacher George Hopper published an online book that sums up the difficulty of the shift, but also its hopefulness. It is called Reluctant Journey – A pilgrimage of faith from homophobia to Christian love.

The struggle against anti-gay prejudice is not just a church one. In pubs, in tabloid newspapers, in homes and workplaces, rejection lurks behind thin facades of liberalism. Evangelical Christians are deeply immersed in the problem. But if they learn from their history and re-read the biblical message in the light of its living centre, Christ, they can be part of a historic change.